Does work function in photoelectric changes with the voltage applied.?

No, the work function of a surface depends on the nature of that surface. It is not affected by the external voltage applied to the surface.

When the voltage across the anode-cathode increases, more electrons can reach the anode. The photo-current will increase with the increase of the applied voltage. A saturation current will occur when ALL emitted electrons are reaching the anode.

Note that photo-electrons emitted from the cathode are NOT of single energy. Some electrons possess higher energy, and some of lower energy. This is due to electrons originally located in different depth below the cathode surface.

The external applied voltage only affect electrons that have already been emitted from the cathode surface.

work fuction not related to the voltage of cathode. it is fixed. that is the enegry required to knock the electron out of the metal surface. The cathode voltage is no help for knocking out the electrons but the photon's energy do it.